No 10 says there are no plans to speed up the introduction of new rules on lobbying in the wake of the row that led to the resignation of Liam Fox. Photograph: Kerim Okten/EPA

Downing Street has said there are no plans to speed up the introduction of new rules on lobbying in the wake of the row that led to the resignation of Liam Fox as defence secretary.

Nick Clegg and other Liberal Democrat ministers are believed to have seen the allegations over the links between Fox and his friend Adam Werritty as an opportunity to ramp up the pressure on their Conservative colleagues to honour a coalition commitment in this parliamentary session to set up a statutory register of lobbyists and ensure "greater transparency".

William Hague, the foreign secretary, said over the weekend that the regulation of lobbyists would be examined after the cabinet secretary, Sir Gus O' Donnell, published his report into Fox's links with Werritty, which is expected on Tuesday.

But despite the series of allegations that emerged last week and that eventually led to Fox's decision to step down on Friday, the prime minister's official spokesman said the government will not accelerate plans to set up a statutory register of lobbyists.

The spokesman said the moves to tighten up lobbying rules were a "separate issue" to O'Donnell's report into the links between Fox and Werritty, his former flatmate and best man.

The deputy prime minister announced 11 months ago that a bill on political and constitutional law, including a statutory register of lobbyists, would be introduced this year.

But Mark Harper, the constitutional reform minister, told MPs last week that legislation would be introduced in the second session, which begins after the Queen's speech in May 2012, following a consultation exercise over the coming months.

Downing Street said at a morning briefing that O'Donnell's report would be "transparent", though it remains unclear whether it would include a list of all the ministerial meetings at which Werritty was present. The report will not include recommendations on policy or procedure because O'Donnell was merely asked to establish the facts.

Werritty is known to have met Fox on at least 40 occasions at the Ministry of Defence in Whitehall and on trips overseas, despite having no official position.

David Cameron's official spokesman said: "If there are any things in that report which we are relevant [to lobbying or other policy] then obviously we will take them into account. It's always been our policy to move to a statutory register. There will be consultation on this shortly and we will legislate after that consultation. The intention would be to legislate in the next session [of parliament]."

Jesse Norman, Conservative MP for Hereford and South Herefordshire South, told BBC Radio 4's World at One programme that lobbying is a "canker" in politics, and warned that undue influence was often imposed by lobbying groups.

Norman said it was understandable why the government had not pursued the lobbying agenda too zealously, but argued the allegations surrounding Fox meant it should be pursued.

"I certainly think the government's had a lot of other things to think about with a global economic crisis, the situation in the eurozone, and all the other problems we've faced. But I do think that this recent turn of events reminds us why it's important for the government to press ahead with this."

He said Werritty would have been subject to greater scrutiny if there were a register of lobbyists.

"Isn't it the case that, as a person representing a charitable or philanthropic organisation, as it was maintained, that he would have been subject to a civil service process to assess whether or not he was a lobbyist, or if not a lobbyist was behaving as one? And that seems to me perfectly reasonable," said Norman.

Police and the Electoral Commission have been asked to investigate allegations that Fox and Werritty committed offences by misleading donors and failing to declare funding.

Moulton was apparently told the firm helped provide "security and analysis" and was unaware it was funding Werritty's travel to meet Fox on official trips.

The millionaire has also complained to the Conservative party about the way he was treated.

There are reports that those giving money to Pargav had been promised anonymity, which may be a breach of laws on declaring donations. An Electoral Commission spokesman said it was considering a complaint that Fox had breached donations legislation.

Bassetlaw Labour MP John Mann has written to police asking for a fraud investigation to be launched.

"Mr Werritty gave out business cards saying he was an adviser to Dr Fox," he said. "If that is not the case and he was getting money – for whatever purpose – by misrepresenting his relationship with the defence secretary, that cannot be right."

Fox's actions should also be scrutinised by the police, he added.

A City of London Police spokesman confirmed the force had received an allegation of fraud.

"Officers from the force's economic crime directorate will consider the matter and establish whether or not it is appropriate to launch an investigation," he said.

Cameron's spokesman on Monday said he was not aware of any approach by police to Downing Street in relation to Werritty.

Fox also faces a potential inquiry by the parliamentary standards commissioner into claims that he let Werritty live rent-free in, and run a business from, a taxpayer-funded property.

The Labour leader, Ed Miliband, said he felt sorry for Fox on a personal level "because he's been through real torment in the last 10 days".

He appeared to concede that Labour's approach in government on lobbying had not worked and backed moves to greater transparency in dealings between politicians and lobbyists.

"I think we do need a register and we do need transparency," he told Boulton and Co show on Sky News.

"We need to be transparent about our contacts with lobbyists. You don't want to create a bureaucratic nightmare, of course, and that would be the concern of civil servants. But there does need to be greater transparency. People have a right to know who we meet and how we meet them, and I'm happy to do that going forward."